Looping menus in Blu-ray can be problematic compared to DVD because of the longer response times for Blu-ray hardware.
One trick that the professionals use is to substantially extend the duration of the menu which means the audio plays, runs out and the menu continues without audio.
If you make it long enough so that users will have selected an option before the menu loops then you’ve effectively achieved what you’re after.
Any Blu-ray authoring tool should allow you to do this.
I haven’t played around with Blu-ray structures yet so I’m not sure if BD-edit can do this for you or not but now that you know what you’re trying to do this might help you figure it out.